Mild wear maps for boundary lubricated contacts

Wear 280–281 (2012) 54–62

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Mild wear maps for boundary lubricated contacts R. Bosman ∗ , D.J. Schipper University of Twente, Drienerlolaan 5, 7500 AE, The Netherlands

a r t i c l e

i n f o

Article history: Received 20 December 2010 Received in revised form 3 August 2011 Accepted 16 January 2012 Available online 24 January 2012 Keywords: Boundary lubrication Sliding wear

a b s t r a c t In this study a model capable of predicting a mild wear map for boundary lubricated contacts is presented and validated using model experiments. Both the transition from mild to severe wear as mild wear itself is modeled. The criterion for the transition from mild to severe wear is a thermal one. The mild wear model is based on the hypothesis that for an additive to protect the surface against severe wear a sacrificial chemical layer should be present at the surface. During the mild wear process the mechanical properties of this layer play a dominant role in the magnitude of the amount of wear. The model is validated using different model experiments showing the influence of the different parameters within the model. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Wear in engineering systems is a problem from a scientific and engineering point of view. Since, for most maintenance operations the machinery needs to be stopped and production is thus delayed. This is in contrast with the increasing demand for smaller more efficient machinery, since it is most profitable to prevent wear by running in the (Elastic) Hydrodynamic Lubrication regime in which no solid–solid contact is occurring. However, if machine components are becoming smaller while carrying the same load the nominal contact pressure increases forcing the components to run in the boundary lubrication regime, in which wear is significantly increased compared to the (E)HL regime [1]. To deal with this problem the lifetime and reliability of a component has to be estimated while running under BL conditions. However, before these steps can be made the type of wear present in the system needs to be determined. For the component to run without failure severe (adhesive) wear needs to be avoided at all time. Therefore, in this article both mild wear, e.g. lifetime estimation, and the transition to severe wear, e.g. instantaneous failure, are dealt with. The latter is modeled using the theory first suggested by Blok in the late thirties [2], who stated that the transition from mild to severe adhesive wear in BL contacts is caused by transcending a critical predefined temperature. However, Blok was not capable of defining a uniform critical temperature for a given combination of lubricant and base material, even for a given system in which only the load and velocity are varied. This was mainly due to the fact that at his time there were no microscopic models available for neither the mechanical nor the thermal calculation.

∗ Corresponding author. Fax: +31 053 489 4784. E-mail address: [email protected] (R. Bosman). 0043-1648/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2012.01.019

Drogen [3] was as one of the first able to identify a uniform critical temperature for a given system and lubricant. However, there was one main shortcoming in this model: mild wear was not included. To validate the model a test setup was designed to apply the load instantaneously, however as this is physically impossible the result was a setup which applied the load at a rate of approximately 150 N/s as depicted in Fig. 1. This implies that before the full load is reached already several meters are slid and mild wear occurred which changes the contact geometry. The wear was first dealt with by both Drogen and Bosman [4] by adapting the macroscopic contact dimensions so the calculated contact radius matches the measured one. This model yielded rather good results; although the change in micro-geometry is not included. To deal with this problem Bosman used a BEM based contact and temperature model combined with the linear wear law of Holm/Archard to include mild wear [5]. This resulted in an improvement in predicting the transition from mild to severe wear. By doing so a simple wear map was created: a mild wear regime with a constant specific wear rate on one side of the transition line and on the other side a severe wear regime where the contact fails as is shown in Fig. 2. However, in real engineering applications the specific wear rate of systems operating in the mild wear regime will not be constant under the different conditions and this issue needs to be dealt with to complete the wear map. In this paper the transition predicted by the thermal threshold is used to identify the regime where the mild wear model presented here is valid, while the mild wear model itself determines the specific wear rate under the different operating conditions. 2. Mild wear model As discussed in Section 1 a mild wear model will be discussed, however first some basic assumption are discussed starting with the application regime of the model, which is the boundary

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Fig. 1. Typical friction and force measurement of a contact situation with direct failure. Solid line force measured and dashed line force used in the numerical model.

lubrication regime in which the system is running under tribochemical wear conditions. In this regime typically chemical products in the lubricant react with the surface material to protect the surface against severe wear by introducing a sacrificial layer of chemical products [6]. This layer is supported by a nano-crystalline layer, which is formed by large plastic deformation under high strain rates and hydrostatic pressure [7–10], forming the complete system schematically presented in Fig. 3. The sacrificial nature of the chemical reaction layer is supported by TEM studies done on wear particles generated by these types of systems running under mild wear conditions [11,12], in these studies the wear particle thickness was typically an order lower than the thickness of the chemical reaction layer present at the surface of the system. A second conclusion may be drawn from these studies, since for the most part the particles found consisted from products originating from the additives added to the lubricant: mild (corrosive) wear originates from shearing off the chemical products formed by the additive package through reaction with base material rather than by direct base material removal. This would imply that if the removal rate of the chemical reaction layer can be evaluated the wear rate of a system can be estimated, making it feasible to estimate the wear rate of a given system. This assumption is also used in [13], only there the statement is used that for the lubricant to able to protect the surface the growth rate should exceed the removal rate: ˙ X˙ ≥ W

(1)

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Fig. 3. Layers present in a run-in system. The top layer is a physically/chemically adsorbed layer which only withstands very mild conditions. The second layer is a chemical layer which is a mixture of oxides and chemical products of the lubricant. The third layer is a nano-crystalline layer formed at the top of the bulk material by severe plastic deformation under large hydrostatic pressure.

This seems in contrast with the thermal transition criterion as stated earlier, however as will be explained shortly the mechanical properties of the chemical reaction layer are greatly influenced by the temperature. It is therefore assumed in the current study that if the critical temperature is reached the mechanical properties of the chemical reaction layer are degenerated so severely it is not able to protect the surface anymore and due to the increase in friction the total surface will fail. The model discussed in [13] is more applicable for the running-in of surfaces where the global contact conditions are less severe and only local failure will occur. In the current model no growth modeling is included and it is assumed that the growth rate is high enough to fulfill Eq. (1) for the complete surface, e.g. the system is running under mild conditions and is fully run-in. The complete wear cycle is graphically represented in Fig. 4. At the first instance of contact the surface is covered with a layer of which the thickness is determined by the chemical balance in the system (hbalance ). Upon contact the layer is stressed and might start yielding, reducing its thickness by (ı). When contact is lost the system will restore the layer thickness. For this process base material will be needed during the chemical reaction, because the layer is built up from both base material and chemical products originating from the additive packages. 3. Tribo chemical layer 3.1. Mechanical model

Fig. 2. Simple wear map, in the mild wear regime the specific wear rate is constant.

To determine the thickness “loss” of the layer (and thus the amount of wear) a few assumptions concerning the mechanical properties of the layer need to be made. First the representative values of the chemical reaction layer are obtained to get a first impression of the type of layer present at the surface. This is done by comparing the different studies done on boundary lubricated contacts lubricated by additive rich lubricants. In this literature study the main focus was on ZDDP/DDP rich lubricants, since the use of these additives is becoming more and more restrictive due to environmental rules, resulting in an increase of the information about properties and wear preventing mechanism of these types of additives. The results from the different studies [6,14–28] concur well with each other and the values for the chemical reacted layers are typically in the range: E = 80 GPa,  = 0.3, and hbalance = 100 nm, suggesting a solid layer on top of the bulk material.

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Fig. 4. (a) Asperities come into contact. (b) Part of the chemical layer is sheared off. (c) Removed film is built up again from bulk and additives. (d) The geometry is changed and wear has occurred.

Next the removal rate of the layer needs to be determined, therefore it is assumed that the removal of the chemical layer is equal to the plastic indentation of the chemical reaction layer. Here only the plastic strains are used in estimating the loss of thickness, since the elastic part of the strains is reversible and thus this part of the indentation will “spring back” as soon as contact is lost, thus restoring the chemical balance of the system without the use of bulk material. This would suggest no wear will occur due to the elastic part of the deformation. However, to be able to calculate the plastic strain, not only the mechanical properties of the layer are needed but also the mechanical behavior of the layer needs to be identified; e.g. does it react as a viscous fluid upon yielding or does it rather react as a solid. In the current study it is stated that the layer will act as a solid rather than a liquid based on the conclusions given in [30], where high frequency indentations were conducted on the layer. Now the mechanical behavior of the layer is identified the stresses present inside the layer need to be determined, since these will be used to determine the plastic strains inside the layer. As discussed earlier the thickness of the layer is very limited compared to the contact patch size, which allows for to the following assumptions. First the layer is in a stress condition where the stresses inside the layer are no function of its thickness (membrane state). Secondly the different contact patches do not interact with each other and can thus be evaluated separately. If now the non-slip and full adherence conditions are used at the interface of the layer and the bulk the pre-stress put on the layer by the bulk material can be expressed as [13]: iilayer =

Elayer 2(1 + layer ) +

of the layer. The hardness of the layer is estimated between 1 and 2 GPa and dependent on the running conditions [23], which in turn can be used to deduct the approximate yield stress of the layer, using the rule of thumb H(ardness) = 2.8yield . 3.2. Temperature effects Another aspect that needs to be taken into consideration is the effect temperature has on the properties of the chemical layer. This is discussed in [32,33], where the first study mainly focuses on the elastic properties rather than on the hardness and the temperatures used are in the range of 80–200 ◦ C. The latter study focuses both on the hardness and elastic properties, however, only a limited range of temperatures ranging from 25 to 80 ◦ C are used. It was concluded in both studies that the Young’s modulus (E) is not significantly affected by the temperature up to a temperature of around 100 ◦ C. At temperatures higher than this the effect of the temperature becomes more pronounced as is represented by the curve given in Fig. 5, of which the equation is given by Eq. (5). Here for the effect of the temperature Tt is set to 325. However, the effect of the temperature on the hardness was more pronounced, especially for low indentation depths as will be the case in the low wear situation [13]. For this reason the slope and “transition

εiibulk

layer Elayer (1 + layer )(1 − 2layer )

(εiibulk + εjjbulk + εkkbulk )

(2)

The stress put on the layer by the “environment” becomes: zzlayer = zzlayer + p

(3)

xzlayer = p

(4)

Combining Eqs. (2)–(4) the total stress state of the layer is defined and a return mapping algorithm combined with a von Mises yield criterion can be used to compute the plastic strains of the layer. However, for a yield criterion to be used a yield stress of the layer needs to be determined, which can be done through the hardness

Fig. 5. Equivalent Young’s modulus E* as a function of the temperature, measurement data are reproduced from [32].

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Fig. 6. Young’s modulus of the chemical film as a function of the hardness (E = E0 + 35(H − H0 ) for H > H0 ) (e.g. the maximum pressure applied to it). Figure is reproduced using the data presented in [34].

point” in Fig. 5 are slightly altered, by setting Tt = 525 to increase the influence of the temperature on the yield strength. CT (T ) =

0.5 − arctan(−2 + (4/1100)(T + Tt )) + 0.05 0.5 − arctan(−2)

(5)

3.3. Anvil Effect A second “external” effect on the properties of the chemical layer is the hardening through hydrostatic pressure called the “Anvil Effect” [34]. This hardening effect is often seen in indentation done in soft amorphous glassy films supported by harder substrates. For the film derived from a ZDDP containing lubricant this effect starts at a threshold pressure of 2 GPa and runs linearly with a slope of 35 as shown in Fig. 6. However, this would then suggest that the Young’s modulus could theoretically exceed the bulk material, which is not realistic. To deal with this issue in the current study a maximum is for the Young’s modulus of the layer is set at 120 GPa as this is the maximum measured value reported in the studied literature. The effect of the pressure on the hardness can be represented by the same slope suggesting a similar behavior. If now the relation between hardness and yield stress is used (H = 2.8yield ) this would render the yield strength as a function of the normal pressure given by:

57

lateral resolution of 1 ␮m × 1 ␮m and the bulk material used is steel with a Young’s modulus of 210 GPa it is shown in [13] that the effect of the chemical reaction layer on the used contact conditions is very limited (less than 3%). Therefore, the effect of the layer needs only to be accounted for in the simulations by lowering the coefficient of friction, while modeling an un-layered system in normal direction. The current stated hypothesis can be interpreted as follows: the bulk material is determining the mechanical conditions which the chemical layer needs to prevail, while the properties of the layer itself determine the amount of wear under these given conditions. Since an un-layered contact model can be used, which are presented widely in literature only a very shortly discussion on the choice of models is giving here and the main mathematical techniques used are discussed for brevity. The interested reader is referred to the dedicated literature mentioned for more details and implementation of the different methods as they are discussed in every detail throughout open literature. The contact model used in the wear model is based on a single loop C(onjugate) G(radient) M(ethod) model first discussed by Polonsky and Keer [36] and later on adapted by Liu et al. [37] to facilitate the D(iscrete)C(onvolution)-F(ast)F(ourier)T(ransformation) algorithm, improving the accuracy while reducing computational times significantly. For the thermal calculations a similar code is used, based upon the theory presented in [38], with the minor adaptation that instead of the direct solver (matrix inversion) method combined with the moving grid method used in the original code the CGM method combined with the DC-FFT algorithm is used to solve the thermal inequalities stated by: T1 (x, y) = T2 (x, y) for x, y ∈ contact

(7)

where T1 (x, y) and T2 (x, y) are the surface temperature of body 1 and body 2 respectively. Q1 (x, y) + Q2 (x, y) = Qtot (x, y) for x, y ∈ contact

(8)

where Q1 (x, y), Q2 (x, y) and Qtot (x, y) are the heat flux into body 1, body 2 and the total heat flux. And the total heat flux is defined by: Qtot (x, y) = P(x, y)V

(9)

where P(x, y) is the normal pressure,  is the coefficient of friction and V is the sliding velocity. 4. Wear rate

If Eq. (6) is fitted to the values reported in literature the value of ˛ would be in the range of 0.1, which is a realistic value also seen in amorphous polymers [35].

If now the contact pressure and displacement the thickness loss of the chemical layer can be determined through the return mapping algorithm. However, of the total thickness loss only a limited percentage is reacted base material and the remaining volume originated from products provided by the oil. When removed only the lost base material will be observed as wear and this needs thus to be estimated to be able to model wear.

3.4. Contact and thermal model

4.1. Chemical composition

To account for all the effects suggested in the preceding subsection and looking at Fig. 3, this would suggest that a layered elasto-plastic contact model is needed, which would significantly complicate the calculations. As the nano-crystalline layer has the same elastic properties as the bulk material this does not need to be taken into account as long as the normal pressure stays in the elastic regime, which is normally the case during mild wear conditions. If the representative values for the chemical layer, as mentioned before, are considered the thickness of the tribo-chemical layer would be in the range of 100 nm and the Young’s modulus in the range of 80 GPa. If these values are combined with the fact that in the simulations presented in this paper typically the input geometries are interference microscopy measurements with a minimum

To obtain a good approximation of the actual amount of base material present throughout the chemical layer, XPS can be used to get an average chemical composition as a function of sputter depth. A typically result of such a test is shown in Fig. 7a where the atomic percentage of the different compounds are given as a function of the depth. This measurement originates from [39] and yields comparable results as given in [17,23]. This good coherence between measurements originating from different authors who used different contact conditions suggest that load and sliding velocity only have a limited effect on the amount of base material inside the tribo-chemical layer. However, as XPS studies only provide the atomic percentage of the layer rather than the volumetric percentage, which is needed, this needs to be deducted. This can be done

layer

layer

yield = yield0 + ˛p for p > ptresh

(6)

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situation by multiplying the volumetric percentage with the total volume removed, which is given by the plastic strain in thickness direction of the chemical layer. 4.2. Incremental sliding However, for each contact calculation this is then only done for one contact instance, e.g. for the exact geometry combination of a stationary contact. Sliding would then be simulated by moving the geometry in sliding direction by an increment size equal to the element size, giving a quasi sliding model. This method would then yield computational times in the range of days to calculate a realistic sliding distance. To solve this issue first the wear rate is determined using a characteristic length. Here the characteristic contact length is based on the assumption that for a contact patch to lose a wear particle it needs to open and close, e.g. encage contact and lose contact again. This would then suggest a characteristic contact length equal to the length of the contact path in sliding direction. As discussed before the total volume which is plastically deformed in thickness direction is assumed to be removed. From this volume the wear percentage is calculated by multiplying it by the volumetric percentage, which is given in Eq. (10). This wear volume is then divided by the characteristic length, which will be determined further on, giving: Kwear (x, y) =

Wperc (ı)ı Wwear hinst (x, y) = = l x yl l

(11)

Here Kwear is the dimensionless wear parameter, hinst the height loss for a single contact instance, ı the plastic indentation of the chemical layer in thickness direction and l the characteristic contact length. This can then be rewritten to a specific wear rate: k(x, y) =

K(x, y) p(x, y)

(12)

which can be used to determine the profile change for each sliding increment: hincrement (x, y) = k(x, y)p(x, y)s = K(x, y)s Fig. 7. Chemical composition of the chemical layer present in the system being studied.

through the total volume per mole of layer material at each depth. This can then be used to divide the volume occupied by base material by and thus giving the volumetric percentage base material as a function of depth. The function resulting from this can then integrated over the plastic indention of the layer and multiplied by the total volume removed. And by doing so the volume base material removed follows. This method is indeed allowed since the film has an amorphous structure and thus the atomic radius gives a good representation of the size of the different atoms. If now the chemical compensation given in Fig. 7 is used the resulting normalized volumetric percentage as a function of indentation/depth becomes: 4.5 × 1019 ı4 − 2.83 × 1013 ı3 + 1.75 × 10−7 ı2 + 0.001ı Wperc (ı) = hbalance (10) Here Wperc is the volumetric percentage base material, ı the plastic indentation of the chemical layer, and hbalance the layer thickness at which the system is in chemical balance. For the systems used in this article it was found that the average film thickness was around 70 nm and the resulting volumetric percentage curve for this particular system is given in Fig. 7b and Eq. (10). Now the volume loss can be calculated for each contact

(13)

5. Experiments To validate the model presented in the preceding sections a different types of experiments are conducted or results obtained from literature are used. The newly conducted experiments are pin on disk experiments using a constant low load and low sliding velocity. In these experiments the roughness of the contacting bodies is varied to be able to validate the different effects influencing wear. And a second set of experiments, obtained from literature [3], using high load pin and high sliding velocities pin on disk tests with variable load and velocity used to validate a transition are used to validate the complete model. 5.1. Experimental procedures For the first set of conditions a smooth ball sliding on a smooth disk is used. Both bodies are made of AISI 52100 steel, of which the material parameters are given in Table 1. The surface geometries of both bodies are shown in Fig. 8a and b. The load and sliding velocity used in the simulation under mild conditions is 10 N combined with Table 1 Material parameters. Material

K [W/mK]  [kg/m3 ] Cp [J/(kg K)] E [GPa] 

AISI 52100 45 Case hardened steel 45

7800 7700

470 467

210 210

H [GPa]

0.3 6.6 0.3 6

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Fig. 8. (a) Surface topography of the ball and (b) of the disk used during the experiments and simulations. (c) Resulting pressure field and (d) temperature field, (e) wear volume after 10 m of sliding.

a velocity of 0.005 m/s as the other parameter of the test are given in Table 2. These conditions not only prevent “severe” wear from occurring it also limits both the contact pressure and temperature so they are in a range where the “Anvil Effect” and thermal effects are not present yet. This can be clearly seen in Fig. 8c and d, where the results of the contact pressure and temperature calculations are presented. This set of conditions offers a change to validate the model using reference values, reducing the risk of using wrong input values for the different parameters influencing wear. The second set of experiments is designed to validate the model for an elliptical contact surface that has been run-in for 4 h, which resulted in an increase in roughness and gives a different roughness orientation. The sliding velocity and load during the running-in

Table 2 Values used in the mild wear test and simulations. Test conditions Fn [N] V [m/s] env [◦ C]  Geometrical entities Rball [m] Rweartrack [m] Rcylinder x , Rcylinder y [m]

10 0.005 25 0.14 2 × 10−3 47 × 10−3 4 × 10−3 , 26.67 × 10−3

procedure were as the normal running conditions, and are presented in Table 2. However, during running in it was observed that the surface run-out, rather than running in, as can be seen in Fig. 9. The disk started with the same surface roughness as shown in Fig. 8 for the smooth ball. Since this process most certainly contains abrasive/plowing wear which is currently not included in the model the run-in surface geometry are taken, which are in the mild wear regime. Due to the surface roughness increase the contact patches are more localized and the pressure is increased to a level above 2 GPa the “Anvil Effect” needs to be considered for the simulations using the roller. Another effect on the roughness is that the roughness orientation is changed toward a roughness oriented mainly in the sliding direction, which would change the characteristic length used in Eq. (11), giving the opportunity to also validate the hypothesis used to obtain the this parameter. The final step is validating the thermal effects on the properties of the chemical layer as proposed. This will be done using measurements presented earlier in [5] of a polished cylinder combined with a hard turned disk. The disk is made of AISI 52100 steel of which the properties are given in Table 1 as are the properties of the case hardened steel for the disk. To validate the model under the most hostile circumstances the measurement point close to the transition point is used as a wear reference and the transition point itself is also predicted to validate the combination of the here proposed wear model in combination with the transition model. However, from

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R. Bosman, D.J. Schipper / Wear 280–281 (2012) 54–62 Table 3 Experimental results and simulation results. Measurement results ball [mm3 /(N m)] kmeasured cylinder kmeasured

8 × 10−9 1.6 × 10−8

3

[mm /(N m)] Calculation results ball [mm3 /(N m)] kcalc cylinder

kcalc

4 × 10−9 9 × 10−9

[mm3 /(N m)]

discussed. The results of the experiments as well as the simulations for a sliding distance of 10 m, which corresponds to approximately half an hour, are presented in Table 3 and Figs. 8e and 9e. For both simulations the same mesh of 256 × 256 elements and 150 sliding increments are used, resulting in a computational time of less than 10 min. As can clearly be seen the calculated value agree very well with the measured one for both contacts, validating the model and the effect pressure has on the properties of the chemical layer. For the high load pin on disk test a critical temperature of 200 ◦ C, a mesh of 240 × 240 elements and 150 sliding increments are used to calculate the transition points. As can be seen in Table 4 the calculated transition points are very close to the measured ones. If the wear widths close to the transition points, shown in Fig. 10, are compared for the different load and velocities it becomes quite clear that there are some differences in the value, however they are in the same range indicating the usefulness of the current model. 6.1. Wear maps

Fig. 9. (a) Surface profile of a roller run for 8 h under the conditions given in Table 2. (b) Counter surface topography. (c) Temperature field in the contact and (d) pressure field in the contact. (e) Resulting wear depth.

the measurement results originating from [3] it can be concluded that not all tests were conducted under boundary lubrication conditions. As for the 400 N measurement the coefficient of friction is in the mixed lubrication regime rather than in the boundary lubrication regime, as shown in Table 4, since this type of contact is currently not included in this study this measurement point is left out of the results. From the measured transition points combined with thermal analyses done in earlier studies a critical temperature of around 200 ◦ C was obtained for the lubricant [5]. 6. Results As a first the experimental results for the low load and sliding velocity of the smooth ball and run-in (rough) elliptical contact are

Finally a complete wear map including the transition from mild to severe wear for both a lubricated line contact (cylinder on disk) and a lubricated run-in elliptical contact are calculated. For these calculations it is assumed that the coefficient of friction within in the mild wear regime is constant. For the run in elliptical contact it is set to 0.15 and for the cylinder on disk setup to 0.1 as these values are good representations of the values obtained during the measurements, see Tables 2 and 3. This yields small difference for the obtained transition points compared with the results given in Table 4. The resulting wear map for the run in elliptical contact is presented in Fig. 11. The wear map consists of a contour plot with lines of constant specific wear rate as a function of normal load and sliding velocity, the so-called “iso-wear” lines. Here it seems not logical that the specific wear rate after decreasing with load it increases again, especially in the low velocity regime. However, this effect can be explained by the hardening effect (“Anvil Effect”) vs. the softening effect caused by the temperature. The combined average effect of the pressure and temperature are presented in Fig. 12b. Here it is also shown in Fig. 12b that the wear volume indeed does increase with increasing load/velocity combination as one expects, however trough the definition of the specific wear rate: k=

W Fs

(14)

the wear rate shows a more unexpected relationship with the normal force and sliding velocity. This can be explained by the average “compensation” through temperature and pressure, as the lines are Table 4 Transition point for a commercial ZDDP oil at room temperature (25 ◦ C). Transition points F [N] Vmeas [m/s] Vcalc [m/s] m 2bmeas [mm] 2bcalc [mm]

700 3.25 3.4 0.100 332 280

550 5.75 5 0.091 390 320

400 9.75 – 0.053 270 –

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Fig. 10. Wear volume expressed as a height profile for (a) a combination of 550 N and 6 m/s and (b) 700 N and 3.5 m/s.

directed almost perpendicular to the transition line. This is due to the fact that first the pressure hardens the layer at high pressures and low speeds and the higher the speed the more pronounced the softening becomes, nullifying the hardening. For the lubricated line contact (cylinder on disk setup) two different simulations are done. One with the load put instantaneously on the new surfaces of which the results are presented in Fig. 13. The second simulation is done with the load profile as shown in Fig. 1 and the resulting wear map is presented in Fig. 14. Here the

Fig. 11. Wear map for the run-in elliptical contact including the specific wear rate.

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Fig. 12. (a) Wear volume vs. sliding velocity and normal force. (b) The combined effect of the temperature and pressure on the elastic properties of the chemical film expressed in a dimensionless relative hardening factor [E/E0 ].

influence of running in becomes quite clear as the transition from mild to severe wear shifts toward higher load/velocity combination. Another interesting phenomenon seen is that the “strange” iso-wear lines are now gone and the lines are laying more along the transition line, this suggest a higher influence of the thermal softening than the mechanical hardening. This probably caused by

Fig. 13. Wear map for the cylinder on disk setup if new surfaces are used with instantaneous load applied.

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Fig. 14. Wear map for the lubricated line contact (cylinder on disk setup) using a linear increase of the normal force as depicted in Fig. 1.

the fact that the in a line contact the heat and pressure is distributed more evenly and the average mechanical properties are thus lowered more compared to concentrated contact is the case as for an elliptical contact. 7. Conclusions In this study a novel model is presented to deal with mild wear in the boundary lubrication regime. The model uses the basic assumption that the improved wear resistance of a contact lubricated with additive rich oil originates from the sacrificial layer formed by the additive package on top of the native oxide layer. Since the thickness of the layer is very limited the model assumes that the “environment” which the layer needs to withstand is determined by the properties of the bulk material, while the mechanical properties of the layer itself determines the amount of material removed. The model is validated for different contact conditions and the results show that the model is capable of predicting the amount of wear occurring in mild wearing systems. To expand the practical implementation of the model it is combined with the theory that the transition from mild to severe wear is a thermal phenomenon. This enables the model to not only estimate the amount of wear present in a system but also if the system will fail, creating a complete wear map. References [1] A. William Ruff, Friction and Wear Data Bank, Modern Tribology Handbook, Two Volume Set, CRC Press, 2000. [2] H. Blok, Seizure delay method for determining the protection against scuffing afforded by extreme pressure lubricants, SAE Journal 44 (1939) 193–204. [3] M.v. Drogen, The transition to adhesive wear of lubricated concentrated contacts, Ph.D. Thesis, University of Twente, 2005, p. 105, www.tr.ctw.utwente.nl. [4] R. Bosman, Mild microscopic wear in the boundary lubrication regimeGeringer mikroskopischer Verschleiß geschmierter Kontakte in Grenzflächen, Materialwissenschaft und Werkstofftechnik 41 (2010) 29–32. [5] R. Bosman, D.J. Schipper, On the transition from mild to severe wear of lubricated, concentrated contacts: the IRG (OECD) transition diagram, Wear 269 (2010) 581–589. [6] M.A. Nicholls, T. Do, P.R. Norton, M. Kasrai, G.M. Bancroft, Review of the lubrication of metallic surfaces by zinc dialkyl-dithiophosphates, Tribology International 38 (2005) 15–39. [7] M. Reichelt, U. Gunst, T. Wolf, J. Mayer, H.F. Arlinghaus, P.W. Gold, Nanoindentation, TEM and ToF-SIMS studies of the tribological layer system of cylindrical roller thrust bearings lubricated with different oil additive formulations, Wear 268 (2010) 1205–1213. [8] D. Shakhvorostov, B. Gleising, R. Büscher, W. Dudzinski, A. Fischer, M. Scherge, Microstructure of tribologically induced nanolayers produced at ultra-low wear rates, Wear 263 (2007) 1259–1265.

[9] D. Shakhvorostov, K. Pohlmann, M. Scherge, Structure and mechanical properties of tribologically induced nanolayers, Wear 260 (2006) 433–437. [10] W. Yan, L. Fang, Z. Zheng, K. Sun, Y. Xu, Effect of surface nanocrystallization on abrasive wear properties in Hadfield steel, Tribology International 42 (2009) 634–641. [11] M.Z. Huq, P.B. Aswath, R.L. Elsenbaumer, TEM studies of anti-wear films/wear particles generated under boundary conditions lubrication, Tribology International 40 (2007) 111–116. [12] M. Scherge, J.M. Martin, K. Pohlmann, Characterization of wear debris of systems operated under low wear-rate conditions, Wear 260 (2006) 458–461. [13] R. Bosman, D.J. Schipper, Running-in of systems protected by additive-rich oils, Tribology Letters 41 (2010) 1–20. [14] M.A. Nicholls, P.R. Norton, G.M. Bancroft, M. Kasrai, T. Do, B.H. Frazer, G.D. Stasio, Nanometer scale chemomechanical characterizaton of antiwear films, Tribology Letters 17 (2003) 205–336. [15] Z. Zhang, Tribofilms generated from ZDDP and DDP on steel surfaces: Part I, Tribology Letters 17 (2005) 211–220. [16] J.P. Ye, S. Araki, M. Kano, Y. Yasuda, Nanometer-scale mechanical/structural properties of molybdenum dithiocarbamate and zinc dialkylsithiophosphate tribofilms and friction reduction mechanism, Japanese Journal of Applied Physics Part 1: Regular Papers Brief Communications & Review Papers 44 (2005) 5358–5361. [17] J.M. Martin, C. Grossiord, T. Le Mogne, S. Bec, A. Tonck, The two-layer structure of zndtp tribofilms. Part 1: AES, XPS and XANES analyses, Tribology International 34 (2001) 523–530. [18] M. Kasrai, S. Marina, B.G. Micheal, Y.E.S.R.P. Ray, X-ray adsorption study of the effect of calcium sulfonate on antiwear film formation generated from neutral and basic ZDDPs: Part 1—Phosporus species, Tribology Transactions 46 (2003) 434–442. [19] M. Aktary, M.T. McDermott, G.A. McAlpine, Morphology and nanomechanical properties of ZDDP antiwear films as a function of tribological contact time, Tribology Letters 12 (2002) 155–162. [20] M.A. Nicholls, G.M. Bancroft, P.R. Norton, M. Kasrai, G. De Stasio, B.H. Frazer, L.M. Wiese, Chemomechanical properties of antiwear films using X-ray absorption microscopy and nanoindentation techniques, Tribology Letters 17 (2004) 245–259. [21] J.P. Ye, M. Kano, Y. Yasuda, Evaluation of nanoscale friction depth distribution in ZDDP and MoDTC tribochemical reacted films using a nanoscratch method, Tribology Letters 16 (2004) 107–112. [22] H.B. Ji, M.A. Nicholls, P.R. Norton, M. Kasrai, T.W. Capehart, T.A. Perry, Y.T. Cheng, Zinc-dialkyl-dithiophosphate antiwear films: dependence on contact pressure and sliding speed, Wear 258 (2005) 789–799. [23] S. Bec, A. Tonck, J.M. Georges, R.C. Coy, J.C. Bell, G.W. Roper, Relationship between mechanical properties and structures of zinc dithiophosphate antiwear films, Proceedings of the Royal Society of London Series A: Mathematical Physical and Engineering Sciences 455 (1999) 4181–4203. [24] K. Komvopoulos, V. Do, E.S. Yamaguchi, P.R. Ryason, Nanomechanical and nanotribological properties of an antiwear tribofilm produced from phosphorus-containing additives on boundary-lubricated steel surfaces, Journal of Tribology: Transactions of the ASME 126 (2004) 775–780. [25] O.L. Warren, Nanomechanical properties of films derived from zinc dialkyldithiophosphate, Tribology Letters 4 (1998) 189–198. [26] C. Minfray, J.M. Martin, C. Esnouf, T. Le Mogne, R. Kersting, B. Hagenhoff, A multi-technique approach of tribofilm characterisation, Thin Solid Films 447 (2004) 272–277. [27] G.M. Bancroft, M. Kasrai, M. Fuller, Z. Yin, K. Fyfe, K.H. Tan, Mechanisms of tribochemical film formation: stabilityof tribo- and thermally-generated ZDDP films, Tribology Letters 3 (1997) 47–51. [28] K. Topolovec-Miklozic, T. Forbus, H. Spikes, Film thickness and roughness of ZDDP antiwear films, Tribology Letters 26 (2007) 161–171. [30] C. Minfray, J.-M. Martin, T. Lubrecht, M. Belin, T.L. Mogne, M.P.G.D.D. Dowson, A novel experimental analysis of the rheology of ZDDP tribofilms Tribology and Interface Engineering Series, Elsevier, 2003, pp. 807–817. [32] G. Pereira, D. Munoz-Paniagua, A. Lachenwitzer, M. Kasrai, P.R. Norton, T.W. Capehart, T.A. Perry, Y.-T. Cheng, A variable temperature mechanical analysis of ZDDP-derived antiwear films formed on 52100 steel, Wear 262 (2007) 461–470. [33] K. Demmou, S. Bec, J.L. Loubet, J.M. Martin, Temperature effects on mechanical properties of zinc dithiophosphate tribofilms, Tribology International 39 (2006) 1558–1563. [34] K. Demmou, S. Bec, J.L. Loubet, Effect of Hydrostatic Pressure on the Elastic Properties of ZDTP Tribofilms, Cornell University Library, 2007. [35] J. Rottler, M.O. Robbins, Yield conditions for deformation of amorphous polymer glasses, Physical Review E 64 (2001) 051801. [36] I.A. Polonsky, L.M. Keer, A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear 231 (1999) 206–219. [37] S. Liu, Q. Wang, G. Liu, A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses, Wear 243 (2000) 101–111. [38] R. Bosman, M.B. de Rooij, Transient thermal effects and heat partition in sliding contacts, Journal of Tribology 132 (2010) 021401. [39] A. Voght, Tribological Reactions Layers in BL Contacts, Bosh-CR, Schillerhohe, 2008.